Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions

Abstract: Using soft-collinear effective theory (SCET), which provides a unified framework for factorization, resummation of logarithms, and incorporation of universal nonperturbative functions in hard-scattering QCD cross-sections, we present a new prediction of angularity distributions in e+e- annihilation. Angularities tau_a are an infinite class of event shapes which vary in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter a<2. We calculate angularity distributions for all a<1 to first order in the strong coupling alpha_s and resum large logarithms in these distributions to next-to-leading logarithmic (NLL) accuracy. Our expressions for the next-to-leading order (NLO) O(alpha_s) partonic jet and soft functions in the factorization theorem for angularity distributions are given for the first time. We employ a model for the nonperturbative soft function with a gap parameter which cancels the renormalon ambiguity in the partonic soft function. We explore the relation between the SCET approach to resummation and past approaches in QCD, and discuss the advantages of the effective theory approach. In addition, we draw from the NLO calculations of the jet and soft functions an intuitive lesson about how factorization breaks down in the effective theory as a->1.

Angularity Distributions in $e^+e^-$ Annihilation Using SCET

The paper "Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions" by Hornig, Lee, and Ovanesyan, provides an in-depth analysis of angularity distributions for $e^+e^-$ annihilation processes using Soft-Collinear Effective Theory (SCET). Angularities are a pivotal class of event shapes that allow for intricate probing of jet substructures, characterized by a continuous parameter $a$ which ranges below 2. The research thus emphasizes calculations for angularities with $a<1$, ensuring infrared safety and successful factorization within the SCET framework.

Technical Overview

Using SCET, the authors offer a comprehensive method for factorization of cross-sections which aids in resummation of logarithms and integration of universal nonperturbative functions. This thorough approach results in accurate predictions of angularity distributions perturbatively to $\mathcal{O}(\alpha_s)$ and resummed to Next-to-Leading Logarithmic (NLL) precision.

Significantly, the paper focuses on the flavors of angularity distributions for all $a<1$, addressing the perturbative and resummation intricacies at Next-to-Leading Order (NLO) by incorporating both nonperturbative effects via convolution with a model for the soft function which includes a gap parameter. This model ensures cancellation of renormalon ambiguities present in the partonic soft function, thus enhancing predictive reliability.

Perturbative and Nonperturbative Approaches

The study advances by resolving perturbative expansions and resummation of angularity distributions using SCET's effective methods, which separate contributions at hard, jet, and soft scales. Factorable soft function models structured to eliminate renormalon ambiguities are seamlessly unified within this framework, guided by constraints derived from scaling relations.

Also crucial to the analysis is the exploration of the breakdown of factorization as $a \to 1$, highlighting the convergence of scaling in collinear and soft modes, which suggests the application boundaries of traditional SCET and necessitates a transition to approaches like SCET$_+$ for certain expressions. Despite this, for practical applications, the research appropriately confines itself to $a<1$, navigating challenges by the SCET's scale-dependent strategy to avoid Landau pole singularities encountered in conventional QCD analyses.

Numerical Results and Methodological Robustness

Through numerical procedures, the study extends analytical predictions onto fixed-order QCD results up to $\mathcal{O}(\alpha_s)$, deriving that matching onto higher-order computations refines the accuracy across the $e^+e^-$ event shape spectrum. Furthermore, the presentation of angularity distributions for diverse values of $a$ elucidates the dependency on jet substructures varying across energy dispersions, offering insights that could be pivotal for robust determinations of $\alpha_s$ and expounding soft nonperturbative corrections within future collider experiments.

In conclusion, this paper provides crucial contributions to theoretical advancements in understanding event-shape distributions, facilitating improved predictive capacities for jet physics, and enhancing the methodology deployable within SCET for analyzing QCD processes across various regimes. The findings underscore the pivotal role angularities play in dissecting jet substructures and inform strategic avenues for further research in effective field theories and nonperturbative QCD approaches.